Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Mean curvature flow of Killing graphs


Authors: J. H. Lira and G. A. Wanderley
Journal: Trans. Amer. Math. Soc. 367 (2015), 4703-4726
MSC (2010): Primary 53C42, 53C44
DOI: https://doi.org/10.1090/S0002-9947-2015-06269-2
Published electronically: February 13, 2015
MathSciNet review: 3335398
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study a Neumann problem related to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. We prove that in a particular case these graphs converge to a trivial minimal graph which contacts the cylinder over the domain orthogonally along its boundary.


References [Enhancements On Off] (What's this?)

  • [1] Maria Calle, Leili Shahriyari, Translating graphs by mean curvature flow in $ M^n\times \mathbb{R}$. arXiv: 1109.5659v1 [math.DG] (2011)
  • [2] Bo Guan, Mean curvature motion of nonparametric hypersurfaces with contact angle condition, Elliptic and parabolic methods in geometry (Minneapolis, MN, 1994), A K Peters, Wellesley, MA, 1996, pp. 47-56. MR 1417947 (98a:58045)
  • [3] Gerhard Huisken, Nonparametric mean curvature evolution with boundary conditions, J. Differential Equations 77 (1989), no. 2, 369-378. MR 983300 (90g:35050), https://doi.org/10.1016/0022-0396(89)90149-6
  • [4] Nicholas J. Korevaar, Maximum principle gradient estimates for the capillary problem, Comm. Partial Differential Equations 13 (1988), no. 1, 1-31. MR 914812 (89d:35061), https://doi.org/10.1080/03605308808820536
  • [5] Gary M. Lieberman, Second order parabolic differential equations, World Scientific Publishing Co. Inc., River Edge, NJ, 1996. MR 1465184 (98k:35003)
  • [6] Bo Guan and Joel Spruck, Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity, Amer. J. Math. 122 (2000), no. 5, 1039-1060. MR 1781931 (2001j:53069)
  • [7] Alexander A. Borisenko and Vicente Miquel, Mean curvature flow of graphs in warped products, Trans. Amer. Math. Soc. 364 (2012), no. 9, 4551-4587. MR 2922601, https://doi.org/10.1090/S0002-9947-2012-05425-0
  • [8] Oliver C. Schnürer and Hartmut R. Schwetlick, Translating solutions for Gauss curvature flows with Neumann boundary conditions, Pacific J. Math. 213 (2004), no. 1, 89-109. MR 2040252 (2005a:53110), https://doi.org/10.2140/pjm.2004.213.89

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C42, 53C44

Retrieve articles in all journals with MSC (2010): 53C42, 53C44


Additional Information

J. H. Lira
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici - Bloco 914, Fortaleza, Ceará, Brasil 60455-900
Email: jorge.lira@mat.ufc.br

G. A. Wanderley
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, CCEN - Campus I, João Pessoa, Paraíba, Brasil 58051-900

DOI: https://doi.org/10.1090/S0002-9947-2015-06269-2
Received by editor(s): October 1, 2012
Received by editor(s) in revised form: March 9, 2013
Published electronically: February 13, 2015
Additional Notes: The first author was partially supported by CNPq and PRONEX/FUNCAP
The second author was partially supported by CAPES
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society